Question 1 –Frank WolfeHints and HelpThe outline of the FW algorithm is as follows:1.Choose an initial solution, x02.For iteration i, evaluate the gradient of the objective function at xi-1, which will be 𝛻???−13.Find the new vector?∗that minimizes the product 𝛻?? ?∗subject to the original constraints.4.Find the value of 𝝀that minimizes the expression 𝒇(𝝀𝒙∗+? − 𝝀 𝒙𝒊−?)using bisection method or golden section method.5.Repeat 2-4 until convergence.Consider the following problem:?𝐢? 𝒇𝒙= (𝒙 − ?)?s.t.−?𝟓 ≤ 𝒙 ≤ ??Solve this problem using MSA and the Frank Wolfe algorithm.
UE Mathematical Programming Formulation and Optimality Conditions?𝑖?𝑖?𝑖?? ?𝑎(?)???𝑎0∀𝑎s.t. ?𝑘??𝑘=???∀?,??𝑘??≥0 ∀𝑘,?,??𝑎=?𝑘??𝛿𝑎𝑘??𝑘??∀𝑎This is the objective function“subject to”These are the constraints**This entire formulation (objective function + constraints) is a “program” (can be called other things as well!) Ameans “for each”•tais the cost function on link a•f is the flow on path k for OD pair rs•q is the demand for OD pair rs•x is the flow on link a